有限p-群研究是有限群论最基础、最重要的分支之一，其终极目标是分类全体有限p-群。有限p-群的极大交换子群是分类有限p-群的关键工具之一。令M(G)为有限p-群G的所有极大交换子群阶的集合。已有研究结果给出了一些|M(G)|=1的有限p-群。关于p-群的Oliver猜想主要产生于局部群论的研究，它有深刻的拓扑和群表示论背景。本项目将以极大交换子群作为主要工具，计划给出|M(G)|=1和2的有限p-群的完整分类，并拟利用该分类检验Oliver猜想对|M(G)|=1和2的有限p-群是否成立。

Finite p-groups play a basic and important role in the finite group theory. The research on them is to classify all finite p-groups and the properties of maximal abelian subgroups of finite p-groups are a key way to such a classification. Let M(G) be the set of orders of all maximal abelian subgroups of a finite p-group G. Some finite p-groups with | M(G) | = 1 were known. Oliver conjecture on p-groups arises from the local group theory and it has a deep background of both topology and group representation theory. In this project, we plan to give a complete classification of finite p-groups with | M(G) | = 1 and 2, and verify whether Oliver conjecture holds for such p-groups or not.